document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135826>Question 135826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi My name is Kaleea<BR>\n" );
document.write( " I have to write a Linear Equation Given Two Points<BR>\n" );
document.write( "            step 1: find the slope<BR>\n" );
document.write( "            step 2: use the two point snd slope in Point-Slope<BR>\n" );
document.write( "            step 3: Solve for Y=mx + b\r<BR>\n" );
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document.write( "Number 1) (1,5) (2,7)\r<BR>\n" );
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document.write( "I have ten problems like this. Can you please work this problem out for me and I will be able to finish the last 9?<BR>\n" );
document.write( "(Show me the work?)<BR>\n" );
document.write( "Thank you.<BR>\n" );
document.write( "cvanmol@aol.com </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99515 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's first identify your points:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B1%5D ALIGN=MIDDLE  ALT=\"P%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >):(1,5)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B2%5D ALIGN=MIDDLE  ALT=\"P%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D ALIGN=MIDDLE  ALT=\"x%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D ALIGN=MIDDLE  ALT=\"y%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >):(2,7)\r<BR>\n" );
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document.write( "That means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=1 ALIGN=MIDDLE  ALT=\"x%5B1%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D=5 ALIGN=MIDDLE  ALT=\"y%5B1%5D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=2 ALIGN=MIDDLE  ALT=\"x%5B2%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D=7 ALIGN=MIDDLE  ALT=\"y%5B2%5D=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 1: Find the slope:\r<BR>\n" );
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document.write( "The slope is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29%29 ALIGN=MIDDLE  ALT=\"m=%28%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Just substitute the coordinate values:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28%285-7%29%2F%281-2%29%29=%28-2%29%2F%28-1%29=2 ALIGN=MIDDLE  ALT=\"m=%28%285-7%29%2F%281-2%29%29=%28-2%29%2F%28-1%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 2:\r<BR>\n" );
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document.write( "Two point form:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=%28%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29%29%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=%28%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29%29%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But notice that the big fraction on the right side of the two-point form is the same as the slope calculation, which allows us to write the point-slope form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-y%5B1%5D=m%28x-x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y-y%5B1%5D=m%28x-x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting, remembering that we said <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2 ALIGN=MIDDLE  ALT=\"m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in step 1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=2%28x-1%29 ALIGN=MIDDLE  ALT=\"y-5=2%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note that once you simplify the big fraction in the two-point form, the two-point and point-slope forms give you identical equations.\r<BR>\n" );
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document.write( "Step 3: Solve for y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=2%28x-1%29 ALIGN=MIDDLE  ALT=\"y-5=2%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5=2x-2 ALIGN=MIDDLE  ALT=\"y-5=2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add 5 to both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B3 ALIGN=MIDDLE  ALT=\"y=2x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check the answer:  If we did this correctly, the x- and y-coordinates of the given points, when substituted into the equation for x and y, will make the equation a true statement.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=2%281%29%2B3=2%2B3=5 ALIGN=MIDDLE  ALT=\"5=2%281%29%2B3=2%2B3=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > True<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7=2%282%29%2B3=4%2B3=7 ALIGN=MIDDLE  ALT=\"7=2%282%29%2B3=4%2B3=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > True\r<BR>\n" );
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document.write( "Both true, answer checks.\r<BR>\n" );
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document.write( "Do the rest of your problems the same way.  Hint: Be extremely cautious with signed numbers.  Another hint:  Check your work for every problem.  If an answer doesn't check, the odds are good that you made a sign error.  Good luck.\r<BR>\n" );
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document.write( "Super-Double-Plus-Extra Credit.  What would have happened if I had identified the points the opposite way in the beginning of this problem, that is, if I had said (1,5) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B2%5D ALIGN=MIDDLE  ALT=\"P%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and (2,7) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5B1%5D ALIGN=MIDDLE  ALT=\"P%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >?  Would I have gotten the same or different results at the end? </SPAN>\n" );
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